Predict the algebraic sign of the entropy change for the...

Predict the algebraic sign of the entropy change for the following reactions. (a) $\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{5}(g)$ (b) $\mathrm{SO}_{2}(g)+\mathrm{CaO}(s) \longrightarrow \mathrm{CaSO}_{3}(s)$ (c) $\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{CO}_{3}(a q)$ (d) $\mathrm{Ni}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{NiCl}_{2}(a q)$

Predict the algebraic sign of the entropy change for the following reactions.
(a) $\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{5}(g)$
(b) $\mathrm{SO}_{2}(g)+\mathrm{CaO}(s) \longrightarrow \mathrm{CaSO}_{3}(s)$
(c) $\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{CO}_{3}(a q)$
(d) $\mathrm{Ni}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{NiCl}_{2}(a q)$

Key Concepts

Entropy

Entropy is a thermodynamic property that measures the degree of randomness or disorder in a system. In chemical reactions, a positive entropy change indicates an increase in disorder, while a negative change signifies a decrease in randomness. This concept is fundamental when evaluating the directionality of spontaneous processes and the energy dispersal during a reaction.

Molecularity and Gas Molecule Count

The number of molecules, particularly in the gaseous state, plays a critical role in determining the entropy change of a reaction. Generally, reactions that result in an increase in the number of gas molecules tend to show a positive entropy change because gases have higher entropy due to their greater freedom of motion. Conversely, reactions that reduce the number of gas molecules typically exhibit a negative entropy change.

Phase Effects on Entropy

Different phases of matter contribute differently to the entropy of a system. Gases exhibit the highest entropy with significant molecular motion, followed by liquids and then solids, which have more ordered structures. A reaction involving a change in the physical state (for example, from gas to solid) will therefore be influenced not only by the number of particles but also by the inherent entropy associated with each phase.

Stoichiometry in Predicting Entropy Change

Analyzing the stoichiometric coefficients of the reactants and products allows one to predict the direction of entropy change. By comparing the relative amounts and states of the substances involved, one can determine if the overall disorder of the system is increasing or decreasing. This approach is particularly useful in predicting the algebraic sign of the entropy change in a chemical reaction.

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